Clusters in Markov Chains via Singular Vectors of Laplacian Matrices

Abstract

Suppose that $T$ is a stochastic matrix. We propose an algorithm for identifying clusters in the Markov chain associated with $T$. The algorithm is recursive in nature, and in order to identify clusters, it uses the sign pattern of a left singular vector associated with the second smallest singular value of the Laplacian matrix $I-T.$ We prove a number of results that justify the algorithm's approach, and illustrate the algorithm's performance with several numerical examples.

41 pages, 10 figures

Cited by in corpus (1)

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